Dissociation between phase and power correlation networks in the human brain is driven by co-occurrent bursts

Well-known haemodynamic resting-state networks are better mirrored in power correlation networks than phase coupling networks in electrophysiological data. However, what do these power correlation networks reflect? We address this long-outstanding question in neuroscience using rigorous mathematical analysis, biophysical simulations with ground truth and application of these mathematical concepts to empirical magnetoencephalography (MEG) data. Our mathematical derivations show that for two non-Gaussian electrophysiological signals, their power correlation depends on their coherence, cokurtosis and conjugate-coherence. Only coherence and cokurtosis contribute to power correlation networks in MEG data, but cokurtosis is less affected by artefactual signal leakage and better mirrors haemodynamic resting-state networks. Simulations and MEG data show that cokurtosis may reflect co-occurrent bursting events. Our findings shed light on the origin of the complementary nature of power correlation networks to phase coupling networks and suggests that the origin of resting-state networks is partly reflected in co-occurent bursts in neuronal activity.

A prominent feature of spontaneous cortical activity during wakefulness is the presence of alpha and beta rhythms. These can be observed in the spectral domain as peaks at ≈ 10 Hz and ≈ 16 Hz, respectively (see Supplementary Figure 1a). To analyse spatial patterns of excess cokurtosis in empirical data, we first quantify spatial patterns of large fluctuations in terms of excess kurtosis in empirical MEG data. We computed the excess kurtosis of source-reconstructed cortical signals at the alpha (≈ 10 Hz) and beta (≈ 16 Hz) peak-frequencies at all cortical regions-of-interest and averaged the obtained values over the 89 subjects. Supplementary Figures 1b and c show the subject-averaged map of excess kurtosis in the alpha and beta frequency band, respectively. In the alpha band, the largest values are observed in the inferior parietal cortical and throughout posterior regions, including visual and auditory cortices and the precuneus, as well as in the somatosensory and primary motor cortices. In contrast, no high values are observed in frontal cortices and there appears to be a strict border formed by the central sulcus. In the beta band, the largest values were observed in the inferior parietal and lateral prefrontal cortices, and in the motor and somatosensory cortices (see Supplementary Figure 1c). The parietal and prefrontal regions constitute the well-known fronto-parietal attention network. In previous studies, this network was extracted from MEG data using either independent component or amplitude envelope correlation analysis, both of which exploit statistical relations between signals from different cortical regions. Our results demonstrate that a higher-cognitive resting-state network, the frontal-partietal attention network, can be detected based on an intrinsic property of the individual signals.
Supplementary Figure 1d shows the distribution of the real part of the signal in the alpha band originating from the left primary somatosensory cortex, which had the highest excess kurtosis. The corresponding distribution obtained from a randomized copy of the MEG sensor data is only shown.
The observed distribution has longer tails than expected from a Gaussian signal with the same mean and variance, i.e. it is super-Gaussian. As an illustration, Figure 1e shows a ten-second epoch of this signal, together with the randomized copy. Both signals were z-scored. The observed signal crosses the three-sigma threshold more frequently than the randomized signal does, which is a manifestation of the signals' super-Gaussian nature.
The observed kurtosis maps were highly reproducible in a separate recording session (see Suppementary Figure 2a and b). To ensure that the subject-averaged maps were not dominated by those of a small number of subjects, we recalculated them after excluding the 20 subjects whose individual maps had the largest Euclidean norms. The spatial correlation between these maps and the original 2 maps was 0.99 (alpha band) and 0.97 (beta band). We also did this by excluding the 20 subjects whose maps had the largest maximal value over all cortical regions, yielding correlation coefficients of 0.99 (alpha band) and 0.98 (beta band). To exclude the possibility that the maps are driven by higher signal-to-noise ratios in posterior regions or are an artifact of the processing steps applied to the MEG sensor signals, we also calculated the maps on randomized MEG sensor signals, which were constructed to have the same cross-spectral matrix as the original signals, but are Gaussian. The obtained maps did not exhibit a clear spatial pattern (see Supplementary Figure 2c  For better visibility, the cortical maps were thresholded at their average values. Reproducibility: The correlation between the vectorized upper triangular parts of the networks obtained from recording sessions 1 and 2 in the alpha band was 1.00 (power correlation), 1.00 (coherence), and 0.95 (cokurtosis). The correlation between the vectorized upper triangular parts of the networks obtained from recording sessions 1 and 2 in the beta band was 1.00 (power correlation), 1.00 (coherence), and 0.94 (cokurtosis). These results demonstrate that the statistical uncertainty in the estimated group-level network matrices is practically zero. The correlation between the seed-based cortical maps obtained from recording sessions 1 and 2 in the alpha band was 1.00 (power correlation), 1.00 (coherence), and 0.95 (cokurtosis). The correlation between the seed-based cortical maps obtained from recording sessions 1 and 2 in the beta band was 1.00 (power correlation), 1.00 (coherence), and 0.94 (cokurtosis).
These results demonstrate that the statistical uncertainty in the estimated seed-based cortical maps is practically zero. Reproducibility: The correlations between the cortical maps obtained from the first and second recording sessions were 0.96 (power correlation), 0.94 (coherence), and 0.96 (cokurtosis), which shows that the maps are highly reproducible across recording sessions.